This walk-through goes through the analysis of a BAMM run on our phylogenetic tree, which is short for Bayesian Analysis of Macroevolutionary Mixtures. This model identifies changes in speciation, extinction, and diversification rates on a tree without any knowledge of tip states or traits, and identifies the most likely number of transitions, where they are likely to occur, and outputs a bunch of other useful things.
From the online documentation of BAMM, we are following Section 8: Analysing BAMM Output with BAMMtools. We have previously ran bamm on our tree. Input information about that run here.
Progress and Results
We have plotted all the “core” shifts on the whole of the phylogenetic tree
Identifies lots of shift configurations, but all of them have low probability
Best model has at ~35 shifts
Have identified areas with a high density of potential shifts
Possibilities
Macroevolutionary cohort analysis. An introduction to this is here and explained in more detail here.
Do we need to re-run the model at different levels of sampled diversity to check if the results are robust?
Load in R packages
First we will load in R packages used and the metadata file used and wrangled in a previous walk-through.
Code
set.seed(42)# load packageslibrary(here)library(caper)library(ggtree)library(ggnewscale)library(RColorBrewer)library(patchwork)library(ape)library(phytools)library(BAMMtools)library(coda)library(MetBrewer)library(fastdivrate) # remotes::install_github("jonchang/fastdivrate")library(nlme)library(emmeans)library(tidyverse)# set where I am in the projecthere::i_am('scripts/sequencing_rpoB/analyses/post_bamm_analysis.qmd')# read in metadatad_meta <-read.csv(here('data/sequencing_rpoB/processed/asv_metadata.csv'))
Lineage through time plot
First we will look at a lineage through time plot of our ultrametric phylogenetic tree.
Code
# load in treetree <-read.tree(here('data/sequencing_rpoB/bamm/rerooted-pruned-chronopl10.tre'))# check is rootedis.rooted(tree)
[1] TRUE
Code
# check is ultrametricis.ultrametric(tree)
[1] TRUE
Code
# grab lineage through time datad_ltt <- ape::ltt.plot.coords(tree) %>%data.frame() %>%mutate(time2 = time +1)# create lineage through time plotggplot(d_ltt, aes(time2, N)) +geom_line() +theme_bw(base_size =14) +labs(x ='Relative time',y ='Number of lineages')
Assess convergence of BAMM run
First we will assess convergence of our MCMC simulation.
Code
# read in mcmc output from bammmcmcout <-read.csv(here("data/sequencing_rpoB/bamm/bamm_1_mcmc_out.txt"), header=TRUE)max(mcmcout$generation)
[1] 26400000
Code
# discard some runs as burnin. We will discard the first 10% of samplesburnstart <-floor(0.4*nrow(mcmcout))postburn <- mcmcout[burnstart:nrow(mcmcout), ]# calculate effective sample sizeeffectiveSize(postburn$N_shifts)
var1
635.6407
Code
effectiveSize(postburn$logLik)
var1
199.9596
In general, we want the effective sample size values to be at least 200 (and 200 is on the low side, but might be reasonable for very large datasets). Both are now close to 200 with a 40% burnin.
Next we can look at the number of potential rate shifts.
Reading event datafile: /Users/danpadfield/Desktop/myxo_diversification/data/sequencing_rpoB/bamm/bamm_1_event_data.txt
...........
Read a total of 1321 samples from posterior
Discarded as burnin: GENERATIONS < 10540000
Analyzing 794 samples from posterior
Setting recursive sequence on tree...
Done with recursive sequence
Code
shift_probs <-summary(edata)
Analyzed 794 posterior samples
Shift posterior distribution:
... omitted 2 rows
22 0.018
23 0.035
24 0.077
25 0.091
26 0.100
27 0.150
28 0.130
29 0.120
30 0.096
31 0.059
32 0.042
... omitted 5 rows
Compute credible set of shift configurations for more information:
See ?credibleShiftSet and ?getBestShiftConfiguration
Code
# plot theseggplot(shift_probs, aes(shifts, prob)) +geom_col(col ='black', fill ='light grey') +theme_bw(base_size =14) +labs(x ='Number of shifts',y ='Probability')
Code
# calculate 95% CIs for the number of shiftsn_shifts_ci <-tibble(mean_shifts =mean(postburn$N_shifts),lower_ci =quantile(postburn$N_shifts, 0.025),upper_ci =quantile(postburn$N_shifts, 0.975))n_shifts_ci
The model has converged, and we also now have a narrow(ish) range of potential values for the number of range shifts (between 23 and 34).
The maintainers or BAMM suggest that (usually) the best overall model from a BAMM analysis is the model with the highest Bayes factor relative to the null model, \(M_{0}\), which has zero rate shifts. However, we do not have any samples of zero shifts in our postburn in sample 20! However, we do have zero shifts in our preburn-in samples as can be seen here 0.
We can therefore calculate Bayes factors from the mcmc_out.txt file. We are not going to have a burnin because otherwise we cannot sample the example of zero shifts.
Bayes factors greater than 20 generally imply strong evidence for one model over another; values greater than 50 are very strong evidence in favour of the numerator model. There is no definitive Bayes factor criterion for “significance”, but many researchers consider values greater than 12 to be consistent with at least some effect.
Code
# list filemcmc_file =here("data/sequencing_rpoB/bamm/bamm_1_mcmc_out.txt")# calculate Bayes Factorsbayes_factors <-computeBayesFactors(mcmc_file, expectedNumberOfShifts=500, burnin=0)# grab the columns for pairwise comparisons between 0 shifts and number of shiftsd_bayes_factors <- bayes_factors[,1] %>%data.frame() %>%rownames_to_column(var ='n_shifts') %>%rename(., bayes_factor =`.`)# we can rank bayes factors and then find the the difference between thesed_bayes_factors <-arrange(d_bayes_factors, desc(bayes_factor)) %>%mutate(diff =c(0, abs(diff(bayes_factor))),cum_diff =cumsum(diff))head(d_bayes_factors)
We can see the best model with 27 shifts is >20 away from the next best model, implying strong evidence that the best fit to the data contains 27 shifts.
BAMMtools also has a function for visualising the prior and posterior simultaneously. This is useful to see what models are not being sampled in the posterior, and also to evaluate how far from the prior the posterior has moved.
Code
# use plotPrior to visualise the prior and posterior simultaneouslyd_prior <-plotPrior(mcmcout, expectedNumberOfShifts=500, burnin =0.4) %>%data.frame() %>% janitor::clean_names() %>%pivot_longer(cols =contains('probs'), names_to ='type', values_to ='prob', names_pattern ="(.*)_probs")
Code
ggplot(d_prior, aes(n_shifts, prob, fill = type)) +geom_bar(col ='black', stat ='identity', position=position_dodge()) +theme_bw(base_size =14) +scale_fill_manual('', values =c('grey', 'black'), labels =c('posterior', 'prior')) +labs(x ='Number of shifts',y ='Probability') +theme(legend.position =c(0.2, 0.8))
We can see that our posterior distribution has shifted from the prior which further reinforces our conclusion that the model has converged.
Plotting results from bamm model
We can now try and plot the mean, model-average diversification rates at any point along every branch of a phylogenetic tree. The standard code to do this takes so long to run that right we will not evaluate the code.
Code
plot.bammdata(edata, lwd=2)
We can calculate the credible shift set that is the set of distinct shift configurations that account for 95% of the probability of the data. Core shifts are those that contribute appreciably to your ability to model the data. Non-core shifts are simply ephemeral shifts that don’t really contribute anything: they are simply what you expect under the prior distribution for rate shifts across the tree.
Code
# calculate credible shift setd_css <-credibleShiftSet(edata, expectedNumberOfShifts =500, threshold =5, set.limit =0.95)# number of distinct configurations in the datad_css$number.distinct
[1] 755
Code
# view more information about the credible setsummary(d_css)
95 % credible set of rate shift configurations sampled with BAMM
Distinct shift configurations in credible set: 755
Frequency of 9 shift configurations with highest posterior probability:
rank probability cumulative Core_shifts
1 0.001259446 0.001259446 18
2 0.001259446 0.002518892 21
3 0.001259446 0.003778338 19
4 0.001259446 0.005037783 20
5 0.001259446 0.006297229 19
6 0.001259446 0.007556675 20
7 0.001259446 0.008816121 18
8 0.001259446 0.010075567 22
9 0.001259446 0.011335013 20
...omitted 746 additional distinct shift configurations
from the credible set. You can access the full set from your
credibleshiftset object
Code
# can plot this credible shift setplot.credibleshiftset(d_css)
Omitted 746 plots
However, as can be seen from the summary, even the single best shift configuration has a really low posterior probability (0.00125). Although the best model supports 27 shifts, not all of these are core shifts. There are only 18-22 core shifts identified in the best model shift configurations here.
For some datasets with large numbers of taxa and rate shifts (e.g., trees with thousands of taxa), all shift configurations may have low probability. There are simply too many parameters in the model to allow a single shift configuration to dominate the credible set. An alternative approach is to extract the shift configuration that maximises the marginal probability of rate shifts along individual branches. This is very similar to the idea of a maximum clade credibility tree in phylogenetic analysis. BAMM has a function maximumShiftCredibility for extracting this shift configuration:
Code
# calculate max shift credibilitymsc_set <-maximumShiftCredibility(edata, maximize='product')# grab the best configuration and plot itmsc_config <-subsetEventData(edata, index = msc_set$sampleindex)plot.bammdata(msc_config, lwd=2)addBAMMshifts(msc_config, cex =2)
This picks a model with 22 rate shifts over the whole tree.
We can try and plot these shifts using ggtree. First we will look at the distribution of speciation rates across the tree. We need to be careful about our colour scale to prevent it being misleading.
Here we also change the tip labels of our tree so they rematch with those from our metadata.
Code
# get mean phylorates that underly the colorised plot produced by plot.bammdata# from here: https://groups.google.com/g/bamm-project/c/W6s38xzm6OU/m/LALF47xVS54J#mbt <- getMeanBranchLengthTree(edata, rate = "speciation")# get the mean branch lengths from the best tree configuration as identified from maximumShiftCredibility mbt2 <-getMeanBranchLengthTree(msc_config, rate ="ndr")# get shift nodes from "best model"shiftnodes <-getShiftNodesFromIndex(edata, index = msc_set$sampleindex)# get treetree_bamm <- mbt2$phy# remove family name from the tip labeld_labels <-data.frame(tip_label = tree_bamm$tip.label) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_', remove =FALSE) %>%unite('tip_label_new', c(part1, part2), sep ='_')tree_bamm$tip.label <- d_labels$tip_label_new# get the edge lengths in a dataframed_tree_bamm <-data.frame(tree_bamm$edge, edge_num=1:nrow(tree_bamm$edge), edge_length = tree_bamm$edge.length)colnames(d_tree_bamm)=c("parent", "node", "edge_num", 'edge_length')# transform these to log for the colour scaled_tree_bamm <-mutate(d_tree_bamm, log_edge_length =log(edge_length))# visualise edge lengths that represent speciation rates of each branch# similar to visualising colour breaks http://bamm-project.org/colorbreaks.html#how-do-i-plot-these-histogramsp1 <-ggplot(d_tree_bamm, aes(edge_length)) +geom_histogram(col ='black', fill ='light grey') +theme_bw()p2 <-ggplot(d_tree_bamm, aes(log(edge_length))) +geom_histogram(col ='black', fill ='light grey') +theme_bw()p1 + p2
We will use the log edge lengths/rates of diversification because they result in a more even spread of diversification rates across a range of values.
Now we can plot the tree. We will try plot the family assignment around the edge of the tree. We also need to assign the colours the same as before.
Code
# constrained familiesconstrained_families <-c('Myxococcaceae', 'Vulgatibacteraceae', 'Anaeromyxobacteraceae', 'Polyangiaceae', 'Sandaracinaceae', 'Nannocystaceae', 'Haliangiaceae')# find the mrca of each of the constrained familiesd_meta2 <-filter(d_meta, family %in% constrained_families) %>% dplyr::select(family, tip_label) %>%group_by(family) %>%nest() %>%mutate(mrca =NA)for(i in1:nrow(d_meta2)){ d_meta2$mrca[i] <-findMRCA(tree_bamm, tips = d_meta2$data[[i]]$tip_label)}d_meta2 <- dplyr::select(d_meta2, family2 = family, mrca) %>%mutate(blank_label ='')# add colour for the different familiescols <-c(colorRampPalette(brewer.pal(11, "Spectral"))(nrow(d_meta2)))names(cols) <-sort(d_meta2$family2)# define colours for the different habitatscols_hab <-met.brewer('Austria', n =7)names(cols_hab) <-c('mud_and_shore', 'freshwater', 'terrestrial', 'freshwater:terrestrial', 'generalist', 'mud_and_shore:terrestrial', 'freshwater:mud_and_shore')hab_labels <-c('marine mud', 'freshwater', 'terrestrial', 'freshwater + terrestrial', 'generalist', 'marine mud + terrestrial', 'freshwater + marine mud')# remove any tip labels not in our tree from d_metad_meta <-filter(d_meta, tip_label %in% tree_bamm$tip.label)# make a separate column for the rare states to make their size bigger!d_meta <-mutate(d_meta, rare =ifelse(habitat_preference %in%c('generalist', 'mud_and_shore:terrestrial'), 'rare', 'common'))# plot tree using ggtree# first colour branches and add rate shiftsp1 <-ggtree(tree_bamm, layout ='circular', branch.length ='none', aes(col = log_edge_length)) %<+% d_tree_bamm +scale_color_gradientn('Net diversification (branch colours)', colors =met.brewer(name='Hiroshige', direction=-1, override.order = F), breaks=c(min(d_tree_bamm$log_edge_length, na.rm =TRUE) +abs(min(d_tree_bamm$log_edge_length, na.rm =TRUE))*0.2, max(d_tree_bamm$log_edge_length, na.rm =TRUE) *0.95), labels=c("Slow","Fast")) +geom_point2(aes(subset=(node %in% shiftnodes)), color="black",size=5)# next add tip pointsp2 <- p1 %<+% d_meta +new_scale_color() +geom_tippoint(aes(x=x+5, col = habitat_preference, size = rare), position =position_jitter(width =3, height =0)) +scale_color_manual('Habitat preference (tip points)', values = cols_hab, labels = hab_labels) +scale_size_manual(values =c(0.6, 2)) +guides(color =guide_legend(override.aes =list(size =5)),size ='none')p2 +new_scale_colour() +geom_cladelab(data = d_meta2,mapping =aes(node = mrca,color = family2,label = blank_label),offset =10,barsize =2) +scale_color_manual('Family (outer bar)', values = cols) +guides(color =guide_legend(override.aes =list(size =5)))
We can look at diversification rates change through time to see if diversification in general is faster or slower deeper in the tree, and therefore further back in evolutionary time.
We can also grab the rates through time for all the sub-trees after a rate shift to see how they compare. To do this we need to write our own function to process the data and get it ready for plotting.
Code
# write function to get rate through time into the correct formatget_rate_through_time_df <-function(ephy, ...){ rtt <-getRateThroughTimeMatrix(ephy, ...)# get dataframe of each part# first speciation rtt_sp <- rtt$lambda %>%data.frame() %>%mutate(sample =1:n()) %>%pivot_longer(starts_with('X'), names_to ='time_point', values_to ='speciation') %>%mutate(time_point =parse_number(time_point)) %>%group_by(sample) %>%mutate(time =unname(rtt$times)) %>%ungroup()# second extinction rtt_ex <- rtt$mu %>%data.frame() %>%mutate(sample =1:n()) %>%pivot_longer(starts_with('X'), names_to ='time_point', values_to ='extinction') %>%mutate(time_point =parse_number(time_point)) %>%group_by(sample) %>%mutate(time =unname(rtt$times)) %>%ungroup() rtt_comb <-left_join(rtt_sp, rtt_ex) rtt_comb <-mutate(rtt_comb, net_div = speciation - extinction) %>%pivot_longer(cols =c(speciation, extinction, net_div), names_to ='process', values_to ='rate')return(rtt_comb)}# get rate through time estimates for the whole treertt_all <-get_rate_through_time_df(ephy = edata)# create meansrtt_combine_means <-group_by(rtt_all, time_point, process, time) %>%summarise(ave_rate =mean(rate), .groups ='drop',lower_ci =quantile(rate, 0.025),upper_ci =quantile(rate, 0.975))# get rate through time estimates for each shift nodertt_shift <-tibble(shift_node = shiftnodes,n =1:length(shiftnodes)) %>%nest(data = shift_node) %>%mutate(temp = purrr::map(data, possibly(~get_rate_through_time_df(ephy = edata, node = .x$shift_node, nodetype ='include'), otherwise =NA_real_)),is_tib = purrr::map_dbl(temp, is_tibble))rtt_shift_nowork <-filter(rtt_shift, is_tib ==0) %>% dplyr::select(data) %>%unnest(data)rtt_shift2 <-filter(rtt_shift, is_tib ==1) %>% dplyr::select(data, temp) %>%unnest(data) %>%unnest(temp)# create meansrtt_shift_means <-group_by(rtt_shift2, time_point, process, time, shift_node) %>%summarise(ave_rate =mean(rate), .groups ='drop',lower_ci =quantile(rate, 0.025),upper_ci =quantile(rate, 0.975))# create a plotggplot() +geom_line(aes(time, ave_rate, group = shift_node), rtt_shift_means, col ='dark grey') +geom_ribbon(aes(time, ymin = lower_ci, ymax = upper_ci, group = shift_node), alpha =0.01, rtt_shift_means, fill ='dark grey') +geom_line(aes(time, ave_rate), rtt_combine_means) +geom_ribbon(aes(time, ymin = lower_ci, ymax = upper_ci), alpha =0.1, rtt_combine_means) +facet_wrap(~process, scales ='free') +theme_bw(base_size =14) +labs(x ='Relative time',y ='rate')
Code
# save plot outggsave(here('plots/sequencing_rpoB/analyses/bamm_rate_through_time.png'), last_plot(), height =5, width =12)
You can see that after a shift node there is generally a rapid acceleration in diversification and speciation rate, after which we see a decline, whereas extinction rate rises quickly and then plateaus through time. The uncertainty around these node specific estimates is very high, but the general pattern appears to hold.
Looking at tip-specific evolutionary rates
We can also estimate tip-specific evolutionary rates. We can plot these across our different traits to see if there is anything particularly interesting going on. This could be complemented by our models looking at state-dependent character diversification rates.
p1 <-ggplot(tip_rates, aes(forcats::fct_reorder(hab_pref_axis, n), speciation)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =12) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='Speciation rate')p2 <-ggplot(tip_rates, aes(forcats::fct_reorder(hab_pref_axis, n), extinction)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =12) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='Extinction rate')p3 <-ggplot(tip_rates, aes(forcats::fct_reorder(hab_pref_axis, n), net_diversification)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =12) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='Net diversification rate')p1 + p2 + p3
Code
# save plot outggsave(here('plots/sequencing_rpoB/analyses/bamm_tip_rates.png'), last_plot(), height =5, width =17)
There does not appear to be much variation between traits in their speciation and extinction rates. If we wanted to follow this further there are lots of papers we could look at. First and foremost would be to read Title & Rabosky’s paper entitled “Tip rates, phylogenies and diversification: What are we estimating, and how good are the estimates?”. They also share other papers that have used tip rate estimates to look at diversification rates across geographical and environmental gradients and across different traits.
We can calculate the DR statistic (also known as tip DR) which is an tip-level estimate of the speciation rate. This measure is non-model based, and incorporates the number of splitting events and the internode distances along the root-to-tip path of a phylogeny, while giving greater weight to branches closer to the present. This was first implemented by Jetz et al. (2012) in their Nature paper about bird diversity in space and time.
Code
# compute tip DRd_tipdr <-DR_statistic_C(tree)# put this into a dataframed_tipdr <-data.frame(tip_label =names(d_tipdr),tip_dr =unname(d_tipdr)) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_') %>%unite('tip_label', c(part1, part2), sep ='_') %>% dplyr::select(-part3) %>%left_join(., dplyr::select(d_meta, tip_label, habitat_preference, hab1, hab2)) %>%filter(!is.na(habitat_preference)) %>%group_by(habitat_preference) %>%mutate(n =n()) %>%ungroup() %>%mutate(hab_pref_axis =gsub(':', '/ ', habitat_preference),hab_pref_axis =gsub('_', ' ', hab_pref_axis))ggplot(d_tipdr, aes(forcats::fct_reorder(hab_pref_axis, n), tip_dr)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =14) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='tip DR (speciation rate)')
This method also shows very little variation in the estimated tip-level speciation rate between traits. It does look like marine mud may have a faster speciation rate than the others. This is interesting because the results from BAMM also indicate marine mud has a higher speciation rate.
This again is something to discuss further with Rutger as I am not sure exactly where to go with the remainder of this analysis. These sorts of statistics may be very useful where fitting of SSE models with rate changes within the state are not possible. This may be something to consider with our dataset where the number of parameters in the MuHiSSE would be so big.
We can can do phylogenetic generalised least squares regressions to account for phylogentic relatedness concerning differences in diversification rate between species with different habitat preferences. This approach has been used by Jetz et al. (2012) in their Nature paper about bird diversity in space and time.
We will first do this using nlme::lme() as described in Liam Revell’s and Luke Harmon’s book “Phylogenetic Comparative Methods in R”.
Code
# remove family name from the tip labeld_labels <-data.frame(tip_label = tree$tip.label) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_', remove =FALSE) %>%unite('tip_label_new', c(part1, part2), sep ='_')tree$tip.label <- d_labels$tip_label_new# set up correlation matrix for the treecor_lambda <-corPagel(value =1, phy = tree, form =~tip_label)# fit phylogenetic generalised linear modelmod <-gls(tip_dr ~ habitat_preference, data = d_tipdr, correlation = cor_lambda)# do contrasts between habitat preferencescontrasts <-emmeans(mod, pairwise ~ habitat_preference)# save out mean branch lengthssaveRDS(mod, here('data/sequencing_rpoB/processed/tipDR_pgls.rds'))saveRDS(contrasts, here('data/sequencing_rpoB/processed/tipDR_pgls_contrasts.rds'))
Code
# remove family name from the tip labeld_labels <-data.frame(tip_label = tree$tip.label) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_', remove =FALSE) %>%unite('tip_label_new', c(part1, part2), sep ='_')tree$tip.label <- d_labels$tip_label_new# set up correlation matrix for the treecor_lambda <-corPagel(value =1, phy = tree, form =~tip_label)# read in modelmod <-readRDS(here('data/sequencing_rpoB/processed/tipDR_pgls.rds'))summary(mod)
# read in contrastscontrasts <-readRDS(here('data/sequencing_rpoB/processed/tipDR_pgls_contrasts.rds'))
So the model fits and is ok. The estimate of Pagel’s lambda - the phylogenetic signal - is 0.83 which is quite high. There are no significant differences between any of the habitat preferences in terms of their speciation rate though.
Defining each tip as either high diversification or low diversification
One of the main questions we are interested in is whether we see a increase in the diversification rate AFTER a transition, but this is a difficult thing to test using either the BAMM model or state-dependent speciation and extinction models.
One alternative might be to create a new variable of high and low diversification rate for each tip, and then combine this with habitat preference when we explore transition rate models.
We can look at the distribution of tip rates, irregardless of habitat preference.
Code
ggplot(tip_rates, aes(net_diversification)) +geom_histogram(fill ='white', col ='black') +theme_bw()
There is a hint that this model is bimodal. We can run a k-means clustering on it to try and split it into two groups.
Code
# do very crude kmeans clusteringmod_clust <-kmeans(tip_rates$net_diversification, 2, algo="Lloyd")# add this to our datasettip_rates <-mutate(tip_rates, cluster =as.character(mod_clust$cluster),div_rate =ifelse(cluster =='1', 'low', 'high'))ggplot(tip_rates, aes(net_diversification, fill = div_rate)) +geom_histogram(col ='black') +theme_bw(base_size =14) +theme(legend.position =c(0.8, 0.8))
We can count the number of each combination of diversification rate (high or low) and each habitat preference to see whether we have some common and rare states.
Code
# check number in each diversity rate bin: high and lowgroup_by(tip_rates, div_rate) %>%tally()
# A tibble: 2 × 2
div_rate n
<chr> <int>
1 high 1142
2 low 2398
# A tibble: 14 × 4
habitat_preference div_rate n prop
<chr> <chr> <int> <dbl>
1 freshwater high 203 0.27
2 freshwater low 556 0.73
3 freshwater:mud_and_shore high 43 0.37
4 freshwater:mud_and_shore low 72 0.63
5 freshwater:terrestrial high 334 0.31
6 freshwater:terrestrial low 755 0.69
7 generalist high 8 0.4
8 generalist low 12 0.6
9 mud_and_shore high 353 0.5
10 mud_and_shore low 349 0.5
11 mud_and_shore:terrestrial high 3 0.15
12 mud_and_shore:terrestrial low 17 0.85
13 terrestrial high 198 0.24
14 terrestrial low 637 0.76
Ok this looks semi-sensible. We will now save this dataset out to try and fit some transition models to the habitat preference by diversification rate bin.
Chapter 13 of Luke Harmon’s book on phylogenetic comparative methods on “Characters and diversification rates”.
Documentation of the R package ggtree used for plotting phylogenies.
Documentation for bamm - Bayesian Analysis of Macroevolutionary Mixtures.
Chapter 3 of Liam Revell and Luke Harmon’s new book on Phylogenetic Comparative Methods in R.
Chapter 6 of Natalie Cooper’s book cover phylogenetic generalised least squares regression in R using caper.
Source Code
---title: "Exploring rates of speciation in the tree using BAMM"author: "Daniel Padfield"date: last-modifiedformat: html: toc: true toc-depth: 2 toc-title: 'Contents' code-overflow: wrap code-fold: true code-tools: true self-contained: true self-contained-math: trueexecute: message: false warning: false fig.align: 'center'editor: visual---## OutlineThis walk-through goes through the analysis of a BAMM run on our phylogenetic tree, which is short for Bayesian Analysis of Macroevolutionary Mixtures. This model identifies changes in speciation, extinction, and diversification rates on a tree without any knowledge of tip states or traits, and identifies the most likely number of transitions, where they are likely to occur, and outputs a bunch of other useful things.From the online documentation of BAMM, we are following [Section 8](http://bamm-project.org/postprocess.html#bammtools): Analysing BAMM Output with BAMMtools. We have previously ran **bamm** on our tree. *Input information about that run here.*## Progress and Results- We have plotted all the "core" shifts on the whole of the phylogenetic tree- Identifies lots of shift configurations, but all of them have low probability- Best model has at \~35 shifts- Have identified areas with a high density of potential shifts## Possibilities- Macroevolutionary cohort analysis. An introduction to this is [here](http://bamm-project.org/rateshifts.html#analysis-of-rate-shifts-in-the-bamm-framework) and explained in more detail [here](https://academic.oup.com/sysbio/article/63/4/610/2848733?login=false).- Do we need to re-run the model at different levels of sampled diversity to check if the results are robust?## Load in R packagesFirst we will load in R packages used and the metadata file used and wrangled in a previous walk-through.```{r load_packages}#| results: falseset.seed(42)# load packageslibrary(here)library(caper)library(ggtree)library(ggnewscale)library(RColorBrewer)library(patchwork)library(ape)library(phytools)library(BAMMtools)library(coda)library(MetBrewer)library(fastdivrate) # remotes::install_github("jonchang/fastdivrate")library(nlme)library(emmeans)library(tidyverse)# set where I am in the projecthere::i_am('scripts/sequencing_rpoB/analyses/post_bamm_analysis.qmd')# read in metadatad_meta <-read.csv(here('data/sequencing_rpoB/processed/asv_metadata.csv'))```## Lineage through time plotFirst we will look at a lineage through time plot of our ultrametric phylogenetic tree.```{r ltt}#| fig.height: 5#| fig.width: 7# load in treetree <-read.tree(here('data/sequencing_rpoB/bamm/rerooted-pruned-chronopl10.tre'))# check is rootedis.rooted(tree)# check is ultrametricis.ultrametric(tree)# grab lineage through time datad_ltt <- ape::ltt.plot.coords(tree) %>%data.frame() %>%mutate(time2 = time +1)# create lineage through time plotggplot(d_ltt, aes(time2, N)) +geom_line() +theme_bw(base_size =14) +labs(x ='Relative time',y ='Number of lineages')```## Assess convergence of BAMM runFirst we will assess convergence of our MCMC simulation.```{r bamm_check_convergence}# read in mcmc output from bammmcmcout <-read.csv(here("data/sequencing_rpoB/bamm/bamm_1_mcmc_out.txt"), header=TRUE)max(mcmcout$generation)# discard some runs as burnin. We will discard the first 10% of samplesburnstart <-floor(0.4*nrow(mcmcout))postburn <- mcmcout[burnstart:nrow(mcmcout), ]# calculate effective sample sizeeffectiveSize(postburn$N_shifts)effectiveSize(postburn$logLik)```In general, we want the effective sample size values to be at least 200 (and 200 is on the low side, but might be reasonable for very large datasets). Both are now close to 200 with a 40% burnin.Next we can look at the number of potential rate shifts.```{r check_rate_shifts}#| fig.height: 4#| fig.width: 6post_probs <-table(postburn$N_shifts) /nrow(postburn)names(post_probs)edata <-getEventData(tree, eventdata =here('data/sequencing_rpoB/bamm/bamm_1_event_data.txt'), burnin =0.4)shift_probs <-summary(edata)# plot theseggplot(shift_probs, aes(shifts, prob)) +geom_col(col ='black', fill ='light grey') +theme_bw(base_size =14) +labs(x ='Number of shifts',y ='Probability')# calculate 95% CIs for the number of shiftsn_shifts_ci <-tibble(mean_shifts =mean(postburn$N_shifts),lower_ci =quantile(postburn$N_shifts, 0.025),upper_ci =quantile(postburn$N_shifts, 0.975))n_shifts_ci```The model has converged, and we also now have a narrow(ish) range of potential values for the number of range shifts (between 23 and 34).The maintainers or BAMM suggest that (usually) the best overall model from a BAMM analysis is the model with the highest Bayes factor relative to the null model, $M_{0}$, which has zero rate shifts. However, we do not have any samples of zero shifts in our postburn in sample `r min(postburn$N_shifts)`! However, we do have zero shifts in our preburn-in samples as can be seen here `r min(mcmcout$N_shifts)`.We can therefore calculate Bayes factors from the `mcmc_out.txt` file. We are not going to have a burnin because otherwise we cannot sample the example of zero shifts.Bayes factors greater than 20 generally imply strong evidence for one model over another; values greater than 50 are very strong evidence in favour of the numerator model. There is no definitive Bayes factor criterion for "significance", but many researchers consider values greater than 12 to be consistent with at least some effect.```{r bamm_bayes_factors}# list filemcmc_file =here("data/sequencing_rpoB/bamm/bamm_1_mcmc_out.txt")# calculate Bayes Factorsbayes_factors <-computeBayesFactors(mcmc_file, expectedNumberOfShifts=500, burnin=0)# grab the columns for pairwise comparisons between 0 shifts and number of shiftsd_bayes_factors <- bayes_factors[,1] %>%data.frame() %>%rownames_to_column(var ='n_shifts') %>%rename(., bayes_factor =`.`)# we can rank bayes factors and then find the the difference between thesed_bayes_factors <-arrange(d_bayes_factors, desc(bayes_factor)) %>%mutate(diff =c(0, abs(diff(bayes_factor))),cum_diff =cumsum(diff))head(d_bayes_factors)```We can see the best model with 27 shifts is \>20 away from the next best model, implying strong evidence that the best fit to the data contains 27 shifts.**BAMMtools** also has a function for visualising the prior and posterior simultaneously. This is useful to see what models are not being sampled in the posterior, and also to evaluate how far from the prior the posterior has moved.```{r plot_prior_posterior}#| fig.height: 5#| fig.width: 7# use plotPrior to visualise the prior and posterior simultaneouslyd_prior <-plotPrior(mcmcout, expectedNumberOfShifts=500, burnin =0.4) %>%data.frame() %>% janitor::clean_names() %>%pivot_longer(cols =contains('probs'), names_to ='type', values_to ='prob', names_pattern ="(.*)_probs")ggplot(d_prior, aes(n_shifts, prob, fill = type)) +geom_bar(col ='black', stat ='identity', position=position_dodge()) +theme_bw(base_size =14) +scale_fill_manual('', values =c('grey', 'black'), labels =c('posterior', 'prior')) +labs(x ='Number of shifts',y ='Probability') +theme(legend.position =c(0.2, 0.8))```We can see that our posterior distribution has shifted from the prior which further reinforces our conclusion that the model has converged.## Plotting results from bamm modelWe can now try and plot the mean, model-average diversification rates at any point along every branch of a phylogenetic tree. The standard code to do this takes so long to run that right we will not evaluate the code.```{r plot_diversification_rates}#| eval: falseplot.bammdata(edata, lwd=2)```We can calculate the credible shift set that is the set of distinct shift configurations that account for 95% of the probability of the data. Core shifts are those that contribute appreciably to your ability to model the data. Non-core shifts are simply ephemeral shifts that don't really contribute anything: they are simply what you expect under the prior distribution for rate shifts across the tree.```{r credible_shift_sets}#| fig.height: 7#| fig.width: 8# calculate credible shift setd_css <-credibleShiftSet(edata, expectedNumberOfShifts =500, threshold =5, set.limit =0.95)# number of distinct configurations in the datad_css$number.distinct# view more information about the credible setsummary(d_css)# can plot this credible shift setplot.credibleshiftset(d_css)```However, as can be seen from the summary, even the single best shift configuration has a really low posterior probability (0.00125). Although the best model supports 27 shifts, not all of these are core shifts. There are only 18-22 core shifts identified in the best model shift configurations here.For some datasets with large numbers of taxa and rate shifts (e.g., trees with thousands of taxa), all shift configurations may have low probability. There are simply too many parameters in the model to allow a single shift configuration to dominate the credible set. An alternative approach is to extract the shift configuration that maximises the marginal probability of rate shifts along individual branches. This is very similar to the idea of a maximum clade credibility tree in phylogenetic analysis. BAMM has a function `maximumShiftCredibility` for extracting this shift configuration:```{r max_clade_cred}#| fig.height: 6#| fig.width: 7# calculate max shift credibilitymsc_set <-maximumShiftCredibility(edata, maximize='product')# grab the best configuration and plot itmsc_config <-subsetEventData(edata, index = msc_set$sampleindex)plot.bammdata(msc_config, lwd=2)addBAMMshifts(msc_config, cex =2)```This picks a model with 22 rate shifts over the whole tree.We can try and plot these shifts using ggtree. First we will look at the distribution of speciation rates across the tree. We need to be careful about our colour scale to prevent it being misleading.Here we also change the tip labels of our tree so they rematch with those from our metadata.```{r plot_ggtree_prep}#| fig.height: 5#| fig.width: 12# get mean phylorates that underly the colorised plot produced by plot.bammdata# from here: https://groups.google.com/g/bamm-project/c/W6s38xzm6OU/m/LALF47xVS54J#mbt <- getMeanBranchLengthTree(edata, rate = "speciation")# get the mean branch lengths from the best tree configuration as identified from maximumShiftCredibility mbt2 <-getMeanBranchLengthTree(msc_config, rate ="ndr")# get shift nodes from "best model"shiftnodes <-getShiftNodesFromIndex(edata, index = msc_set$sampleindex)# get treetree_bamm <- mbt2$phy# remove family name from the tip labeld_labels <-data.frame(tip_label = tree_bamm$tip.label) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_', remove =FALSE) %>%unite('tip_label_new', c(part1, part2), sep ='_')tree_bamm$tip.label <- d_labels$tip_label_new# get the edge lengths in a dataframed_tree_bamm <-data.frame(tree_bamm$edge, edge_num=1:nrow(tree_bamm$edge), edge_length = tree_bamm$edge.length)colnames(d_tree_bamm)=c("parent", "node", "edge_num", 'edge_length')# transform these to log for the colour scaled_tree_bamm <-mutate(d_tree_bamm, log_edge_length =log(edge_length))# visualise edge lengths that represent speciation rates of each branch# similar to visualising colour breaks http://bamm-project.org/colorbreaks.html#how-do-i-plot-these-histogramsp1 <-ggplot(d_tree_bamm, aes(edge_length)) +geom_histogram(col ='black', fill ='light grey') +theme_bw()p2 <-ggplot(d_tree_bamm, aes(log(edge_length))) +geom_histogram(col ='black', fill ='light grey') +theme_bw()p1 + p2```We will use the log edge lengths/rates of diversification because they result in a more even spread of diversification rates across a range of values.Now we can plot the tree. We will try plot the family assignment around the edge of the tree. We also need to assign the colours the same as before.```{r plot_ggtree}#| fig.height: 12#| fig.width: 12# constrained familiesconstrained_families <-c('Myxococcaceae', 'Vulgatibacteraceae', 'Anaeromyxobacteraceae', 'Polyangiaceae', 'Sandaracinaceae', 'Nannocystaceae', 'Haliangiaceae')# find the mrca of each of the constrained familiesd_meta2 <-filter(d_meta, family %in% constrained_families) %>% dplyr::select(family, tip_label) %>%group_by(family) %>%nest() %>%mutate(mrca =NA)for(i in1:nrow(d_meta2)){ d_meta2$mrca[i] <-findMRCA(tree_bamm, tips = d_meta2$data[[i]]$tip_label)}d_meta2 <- dplyr::select(d_meta2, family2 = family, mrca) %>%mutate(blank_label ='')# add colour for the different familiescols <-c(colorRampPalette(brewer.pal(11, "Spectral"))(nrow(d_meta2)))names(cols) <-sort(d_meta2$family2)# define colours for the different habitatscols_hab <-met.brewer('Austria', n =7)names(cols_hab) <-c('mud_and_shore', 'freshwater', 'terrestrial', 'freshwater:terrestrial', 'generalist', 'mud_and_shore:terrestrial', 'freshwater:mud_and_shore')hab_labels <-c('marine mud', 'freshwater', 'terrestrial', 'freshwater + terrestrial', 'generalist', 'marine mud + terrestrial', 'freshwater + marine mud')# remove any tip labels not in our tree from d_metad_meta <-filter(d_meta, tip_label %in% tree_bamm$tip.label)# make a separate column for the rare states to make their size bigger!d_meta <-mutate(d_meta, rare =ifelse(habitat_preference %in%c('generalist', 'mud_and_shore:terrestrial'), 'rare', 'common'))# plot tree using ggtree# first colour branches and add rate shiftsp1 <-ggtree(tree_bamm, layout ='circular', branch.length ='none', aes(col = log_edge_length)) %<+% d_tree_bamm +scale_color_gradientn('Net diversification (branch colours)', colors =met.brewer(name='Hiroshige', direction=-1, override.order = F), breaks=c(min(d_tree_bamm$log_edge_length, na.rm =TRUE) +abs(min(d_tree_bamm$log_edge_length, na.rm =TRUE))*0.2, max(d_tree_bamm$log_edge_length, na.rm =TRUE) *0.95), labels=c("Slow","Fast")) +geom_point2(aes(subset=(node %in% shiftnodes)), color="black",size=5)# next add tip pointsp2 <- p1 %<+% d_meta +new_scale_color() +geom_tippoint(aes(x=x+5, col = habitat_preference, size = rare), position =position_jitter(width =3, height =0)) +scale_color_manual('Habitat preference (tip points)', values = cols_hab, labels = hab_labels) +scale_size_manual(values =c(0.6, 2)) +guides(color =guide_legend(override.aes =list(size =5)),size ='none')p2 +new_scale_colour() +geom_cladelab(data = d_meta2,mapping =aes(node = mrca,color = family2,label = blank_label),offset =10,barsize =2) +scale_color_manual('Family (outer bar)', values = cols) +guides(color =guide_legend(override.aes =list(size =5)))ggsave(here('plots/sequencing_rpoB/analyses/bamm_tree.png'), last_plot(), height =9, width =12)```## Rate variation through timeWe can look at diversification rates change through time to see if diversification in general is faster or slower deeper in the tree, and therefore further back in evolutionary time.We can also grab the rates through time for all the sub-trees after a rate shift to see how they compare. To do this we need to write our own function to process the data and get it ready for plotting.```{r get_rate_through_time}#| fig.height: 5#| fig.width: 17# write function to get rate through time into the correct formatget_rate_through_time_df <-function(ephy, ...){ rtt <-getRateThroughTimeMatrix(ephy, ...)# get dataframe of each part# first speciation rtt_sp <- rtt$lambda %>%data.frame() %>%mutate(sample =1:n()) %>%pivot_longer(starts_with('X'), names_to ='time_point', values_to ='speciation') %>%mutate(time_point =parse_number(time_point)) %>%group_by(sample) %>%mutate(time =unname(rtt$times)) %>%ungroup()# second extinction rtt_ex <- rtt$mu %>%data.frame() %>%mutate(sample =1:n()) %>%pivot_longer(starts_with('X'), names_to ='time_point', values_to ='extinction') %>%mutate(time_point =parse_number(time_point)) %>%group_by(sample) %>%mutate(time =unname(rtt$times)) %>%ungroup() rtt_comb <-left_join(rtt_sp, rtt_ex) rtt_comb <-mutate(rtt_comb, net_div = speciation - extinction) %>%pivot_longer(cols =c(speciation, extinction, net_div), names_to ='process', values_to ='rate')return(rtt_comb)}# get rate through time estimates for the whole treertt_all <-get_rate_through_time_df(ephy = edata)# create meansrtt_combine_means <-group_by(rtt_all, time_point, process, time) %>%summarise(ave_rate =mean(rate), .groups ='drop',lower_ci =quantile(rate, 0.025),upper_ci =quantile(rate, 0.975))# get rate through time estimates for each shift nodertt_shift <-tibble(shift_node = shiftnodes,n =1:length(shiftnodes)) %>%nest(data = shift_node) %>%mutate(temp = purrr::map(data, possibly(~get_rate_through_time_df(ephy = edata, node = .x$shift_node, nodetype ='include'), otherwise =NA_real_)),is_tib = purrr::map_dbl(temp, is_tibble))rtt_shift_nowork <-filter(rtt_shift, is_tib ==0) %>% dplyr::select(data) %>%unnest(data)rtt_shift2 <-filter(rtt_shift, is_tib ==1) %>% dplyr::select(data, temp) %>%unnest(data) %>%unnest(temp)# create meansrtt_shift_means <-group_by(rtt_shift2, time_point, process, time, shift_node) %>%summarise(ave_rate =mean(rate), .groups ='drop',lower_ci =quantile(rate, 0.025),upper_ci =quantile(rate, 0.975))# create a plotggplot() +geom_line(aes(time, ave_rate, group = shift_node), rtt_shift_means, col ='dark grey') +geom_ribbon(aes(time, ymin = lower_ci, ymax = upper_ci, group = shift_node), alpha =0.01, rtt_shift_means, fill ='dark grey') +geom_line(aes(time, ave_rate), rtt_combine_means) +geom_ribbon(aes(time, ymin = lower_ci, ymax = upper_ci), alpha =0.1, rtt_combine_means) +facet_wrap(~process, scales ='free') +theme_bw(base_size =14) +labs(x ='Relative time',y ='rate')# save plot outggsave(here('plots/sequencing_rpoB/analyses/bamm_rate_through_time.png'), last_plot(), height =5, width =12)```You can see that after a shift node there is generally a rapid acceleration in diversification and speciation rate, after which we see a decline, whereas extinction rate rises quickly and then plateaus through time. The uncertainty around these node specific estimates is very high, but the general pattern appears to hold.## Looking at tip-specific evolutionary ratesWe can also estimate tip-specific evolutionary rates. We can plot these across our different traits to see if there is anything particularly interesting going on. This could be complemented by our models looking at state-dependent character diversification rates.```{r tip_rates}#| fig.height: 5#| fig.width: 17# grab out tip rates tip_rates <-data.frame(tip_label = edata$tip.label,speciation = edata$meanTipLambda,extinction = edata$meanTipMu) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_') %>%unite('tip_label', c(part1, part2), sep ='_') %>% dplyr::select(-part3) %>%left_join(., dplyr::select(d_meta, tip_label, habitat_preference, hab1, hab2)) %>%filter(!is.na(habitat_preference)) %>%group_by(habitat_preference) %>%mutate(n =n()) %>%ungroup() %>%mutate(hab_pref_axis =gsub(':', '/ ', habitat_preference),hab_pref_axis =gsub('_', ' ', hab_pref_axis),net_diversification = speciation - extinction)# check numbers are rightgroup_by(tip_rates, habitat_preference) %>%tally() %>%arrange(n)p1 <-ggplot(tip_rates, aes(forcats::fct_reorder(hab_pref_axis, n), speciation)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =12) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='Speciation rate')p2 <-ggplot(tip_rates, aes(forcats::fct_reorder(hab_pref_axis, n), extinction)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =12) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='Extinction rate')p3 <-ggplot(tip_rates, aes(forcats::fct_reorder(hab_pref_axis, n), net_diversification)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =12) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='Net diversification rate')p1 + p2 + p3# save plot outggsave(here('plots/sequencing_rpoB/analyses/bamm_tip_rates.png'), last_plot(), height =5, width =17)```There does not appear to be much variation between traits in their speciation and extinction rates. If we wanted to follow this further there are lots of papers we could look at. First and foremost would be to read Title & Rabosky's paper entitled ["Tip rates, phylogenies and diversification: What are we estimating, and how good are the estimates?"](https://besjournals.onlinelibrary.wiley.com/doi/10.1111/2041-210X.13153). They also share other papers that have used tip rate estimates to look at diversification rates across geographical and environmental gradients and across different traits.We can calculate the DR statistic (also known as tip DR) which is an tip-level estimate of the speciation rate. This measure is non-model based, and incorporates the number of splitting events and the internode distances along the root-to-tip path of a phylogeny, while giving greater weight to branches closer to the present. This was first implemented by Jetz *et al.* (2012) in their Nature paper about bird diversity in space and time.```{r tip_dr}#| fig.height: 5#| fig.width: 7#| warning: false# compute tip DRd_tipdr <-DR_statistic_C(tree)# put this into a dataframed_tipdr <-data.frame(tip_label =names(d_tipdr),tip_dr =unname(d_tipdr)) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_') %>%unite('tip_label', c(part1, part2), sep ='_') %>% dplyr::select(-part3) %>%left_join(., dplyr::select(d_meta, tip_label, habitat_preference, hab1, hab2)) %>%filter(!is.na(habitat_preference)) %>%group_by(habitat_preference) %>%mutate(n =n()) %>%ungroup() %>%mutate(hab_pref_axis =gsub(':', '/ ', habitat_preference),hab_pref_axis =gsub('_', ' ', hab_pref_axis))ggplot(d_tipdr, aes(forcats::fct_reorder(hab_pref_axis, n), tip_dr)) + MicrobioUoE::geom_pretty_boxplot(col='black', fill ='black') +geom_point(shape =21, fill ='white', position =position_jitter(width =0.2)) +theme_bw(base_size =14) +scale_x_discrete(labels = scales::label_wrap(13)) +labs(x ='Habitat preference',y ='tip DR (speciation rate)')```This method also shows very little variation in the estimated tip-level speciation rate between traits. It does look like marine mud may have a faster speciation rate than the others. This is interesting because the results from BAMM also indicate marine mud has a higher speciation rate.This again is something to discuss further with Rutger as I am not sure exactly where to go with the remainder of this analysis. These sorts of statistics may be very useful where fitting of SSE models with rate changes within the state are not possible. This may be something to consider with our dataset where the number of parameters in the MuHiSSE would be so big.We can can do phylogenetic generalised least squares regressions to account for phylogentic relatedness concerning differences in diversification rate between species with different habitat preferences. This approach has been used by Jetz *et al.* (2012) in their Nature paper about bird diversity in space and time.We will first do this using **nlme::lme()** as described in Liam Revell's and Luke Harmon's book "Phylogenetic Comparative Methods in R".```{r pgls_nlme_run}#| eval: false# remove family name from the tip labeld_labels <-data.frame(tip_label = tree$tip.label) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_', remove =FALSE) %>%unite('tip_label_new', c(part1, part2), sep ='_')tree$tip.label <- d_labels$tip_label_new# set up correlation matrix for the treecor_lambda <-corPagel(value =1, phy = tree, form =~tip_label)# fit phylogenetic generalised linear modelmod <-gls(tip_dr ~ habitat_preference, data = d_tipdr, correlation = cor_lambda)# do contrasts between habitat preferencescontrasts <-emmeans(mod, pairwise ~ habitat_preference)# save out mean branch lengthssaveRDS(mod, here('data/sequencing_rpoB/processed/tipDR_pgls.rds'))saveRDS(contrasts, here('data/sequencing_rpoB/processed/tipDR_pgls_contrasts.rds'))``````{r pgls_nlme}# remove family name from the tip labeld_labels <-data.frame(tip_label = tree$tip.label) %>%separate(., tip_label, c('part1', 'part2', 'part3'), sep ='_', remove =FALSE) %>%unite('tip_label_new', c(part1, part2), sep ='_')tree$tip.label <- d_labels$tip_label_new# set up correlation matrix for the treecor_lambda <-corPagel(value =1, phy = tree, form =~tip_label)# read in modelmod <-readRDS(here('data/sequencing_rpoB/processed/tipDR_pgls.rds'))summary(mod)# read in contrastscontrasts <-readRDS(here('data/sequencing_rpoB/processed/tipDR_pgls_contrasts.rds'))```So the model fits and is ok. The estimate of Pagel's lambda - the phylogenetic signal - is 0.83 which is quite high. There are no significant differences between any of the habitat preferences in terms of their speciation rate though.## Defining each tip as either high diversification or low diversificationOne of the main questions we are interested in is whether we see a increase in the diversification rate AFTER a transition, but this is a difficult thing to test using either the BAMM model or state-dependent speciation and extinction models.One alternative might be to create a new variable of high and low diversification rate for each tip, and then combine this with habitat preference when we explore transition rate models.We can look at the distribution of tip rates, irregardless of habitat preference.```{r tip_rate_dist}#| fig.height: 5#| fig.width: 7ggplot(tip_rates, aes(net_diversification)) +geom_histogram(fill ='white', col ='black') +theme_bw()```There is a hint that this model is bimodal. We can run a k-means clustering on it to try and split it into two groups.```{r split_tip_rate}#| fig.height: 5#| fig.width: 7# do very crude kmeans clusteringmod_clust <-kmeans(tip_rates$net_diversification, 2, algo="Lloyd")# add this to our datasettip_rates <-mutate(tip_rates, cluster =as.character(mod_clust$cluster),div_rate =ifelse(cluster =='1', 'low', 'high'))ggplot(tip_rates, aes(net_diversification, fill = div_rate)) +geom_histogram(col ='black') +theme_bw(base_size =14) +theme(legend.position =c(0.8, 0.8))```We can count the number of each combination of diversification rate (high or low) and each habitat preference to see whether we have some common and rare states.```{r check_numbers}# check number in each diversity rate bin: high and lowgroup_by(tip_rates, div_rate) %>%tally()# check per diversity rate bin/habitat preference combinationgroup_by(tip_rates, habitat_preference, div_rate) %>%tally() %>%group_by(habitat_preference) %>%mutate(prop =round(n/sum(n), 2)) %>%ungroup()```Ok this looks semi-sensible. We will now save this dataset out to try and fit some transition models to the habitat preference by diversification rate bin.```{r save_out}saveRDS(dplyr::select(tip_rates, tip_label, div_rate), here('data/sequencing_rpoB/processed/div_rate_bins.rds'))```## Useful links used- [Chapter 13](https://lukejharmon.github.io/pcm/chapter13_chardiv/#ref-Beaulieu2016-ww) of Luke Harmon's book on phylogenetic comparative methods on "Characters and diversification rates".- [Documentation](https://yulab-smu.top/treedata-book/) of the R package **ggtree** used for plotting phylogenies.- [Documentation](http://bamm-project.org/introduction.html#bayesian-analysis-of-macroevolutionary-mixtures) for bamm - Bayesian Analysis of Macroevolutionary Mixtures.- Chapter 3 of Liam Revell and Luke Harmon's new book on Phylogenetic Comparative Methods in R.- [Chapter 6](https://nhcooper123.github.io/pcm-primer-online/phylogenetic-generalised-least-squares-pgls-in-r.html) of Natalie Cooper's book cover phylogenetic generalised least squares regression in R using caper.
